I went back and forth as to whether to pin this question to a specific program of a specific, major version of GIS software. Given the amount of change to the ux, I think ArcGIS Desktop 10 should get its own Tips and Tricks question and will be a great resource for new ArcGIS users and ArcGIS 10 users upgrading from 9.3.

I like the new create feature templates in ArcGIS 10, but if you prefer the old method, you can revert by setting by running ArcGIS\Desktop10.0\Utilities\AdvancedArcMapSettings.exe, clicking the Editor tab, and unchecking Create features using templates and restarting ArcMap.

This isn't a UI tip but it most certainly applies to ArcGIS 10. If you're a developer of extensions then you must use ESRI's new registration model; specifically you'll need to use the ESRIRegAsm utility. More info here.

Customize window has dozens of tools that are not exposed via GP tools or as buttons on toolbars, so you have to add them manually. There are very many useful tools that many experienced Arc users are not familiar with.

Here is my top list of "hidden" tools:

Load Objects - this tool lets you load features into a
feature class from another feature class while respecting certain
mapping and geodatabase behavior rules.

Eye Dropper - this tool can be used to click a color in your map
display and determine its RGB values.

Prepare window (10.1+) - this panel lets you check if there are
any issues that could potentially influence the map performance (like
you had in 9.3 - for Map Service Publishing toolbar). You don't have
to run File > Share as > Service to activate the Prepare window. You
can analyze any map for potential problems with just ArcMap.

"The problem is to make ArcMap run faster it would have to be re-architected and re-engineered, something ESRI will not do because it would be too expensive. The reasons why it is slow now is because 1) the entire software is implemented in COM (big mistake), 2) there are way too many DLLs in the system, and 3) many ESRI engineers do have a clue on how to write software that has performance in mind. " from James Fees Comments MikeC spatiallyadjusted.com/2010/06/18/…
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Mapperz♦Sep 18 '10 at 19:56

1

"do" --> "do not", I presume. (It seems unfair to speculate about the programmers in this way. Surely the ultimate decisions about performance are marketing driven and determined by the person who controls the company.)
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whuber♦Sep 27 '10 at 18:20

If you're on 10.1 or higher, and have a PC that supports multithreading/multiple processes, take advantage of the parallel processing environment. The results vary from tool to tool but overall, it should give you a boost if you have any type of multicore/multithreaded computer.

If your field calculator isn't working and fails with a "There was a failure during processing, check the Geoprocessing Results window for details.", check for a forward slash in the layer name. video: http://drop.io/w1nca2k

"There was a failure during processing, check the Geoprocessing Results window for details.", this also happens if a field name of the layer that you are field_calculating has a trailling "" underscore. Remove the "" and it works as it should.

The default setting of ArcMap does not necessarily expose those buttons you have to drill down to in the context menu. It would be great to have these on the tool bars.

For example you may have created multiple selections on layers in a map document and want to clear all selections. You would typically right click on the layer in the TOC go to Selection and then Clear Selected Features (3 button clicks) or fiddle around with the layers in the list by selection panel in the TOC.

Well that button can be added to any tool bar using the customize window as Alex mentions above. You can now clear all the selections with a single click.

Another button I always add is the continuous zoom/pan button.

Finally the SWIPE button on the effects tool bar is a crowd pleaser and usually blows people away for some reason... :)